Finite Group Databasebeta

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C22×C3×C5×C64 #72183397

order3840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 24576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C5×C64
multiplicative(ℤ/6369)ˣ, (ℤ/7936)ˣ, (ℤ/8492)ˣ, (ℤ/12738)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C23×C3×C5
socle, prime radicalC23×C3×C5C32
LCSG ▷ C1
UCSC1 ◁ G

284 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C128, C2×C3×C4×C5×C64, C23×C3×C5×C64, …
maximal normal subgroup ofC22×C3×C5×C128, C2×C3×C4×C5×C64, C23×C3×C5×C64, …
maximal quotient ofC22×C3×C5×C128, C2×C3×C4×C5×C64, C23×C3×C5×C64, …
automorphism group ofC3×C11×C193, C31×C256, C4×C11×C193
outer automorphism group ofC3×C11×C193, C31×C256, C4×C11×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.